This game has two players: the companies Acme and Initech. Both companies serve
ID: 1124350 • Letter: T
Question
This game has two players: the companies Acme and Initech. Both companies serve the same market. Their cost per unit produced is $2. They have a choice when setting price. They can either choose a high price of $10 per unit or a low price of $5 per unit. If both players set a high price, total demand equals 10,000 units sold. This would be split evenly between Acme and Initech. When both set a low price, total demand is 18,000 units, which is also split evenly. If one of the players sets a low price and the other a high price, the low priced company realizes a demand of 15,000 units and the high priced company only sells 2,000 units.
A) Construct a pay-off matrix for this scenario showing the profits of each company using the various pricing scenarios.
B) Assume that each company pursues its best individual outcome not knowing the choice of the other company. Does this result in more or less profits for the company if this scenario occurs? Explain.
Explanation / Answer
Case 1 : When both set high price = $10, then demand = 10,000.
Each firm’s profit = 0.5*(10-2)*10,000 = $40,000
Case 2: When both set low price = $5, then demand = 18,000
Each firm’s profit = 0.5*(5-2)*18000 = $27,000
Case 3 & 4: When one sets low price and other high price –
Profit firm that sets low price = (5 -2)*15000 = 45000
Profit firm that sets high price = (10 -2)*2000 = 16000
A) Below is payoff matrix -
If Initech plays low price, then Acme will opt to play low price
If Initech plays high price, then Acne will play low price.
Thus Acme will play low price no matter what Initech plays.
Likewise, Initech will also play on low price no matter what Acme plays.
The nash eq is to keep prices low. This scenario offers better pay off than having a cartel where both charge a high price.
Initech low price high price Acme low price (40000 , 40000) (45000, 16000) high price (16000 , 45000) (27000 , 27000)Related Questions
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